Question: Solve for $x$ and $y$ using elimination. ${3x-6y = 12}$ ${-2x+5y = -7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $3$ ${6x-12y = 24}$ $-6x+15y = -21$ Add the top and bottom equations together. $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {3x-6y = 12}\thinspace$ to find $x$ ${3x - 6}{(1)}{= 12}$ $3x-6 = 12$ $3x-6{+6} = 12{+6}$ $3x = 18$ $\dfrac{3x}{{3}} = \dfrac{18}{{3}}$ ${x = 6}$ You can also plug ${y = 1}$ into $\thinspace {-2x+5y = -7}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(1)}{= -7}$ ${x = 6}$